Aircraft: BEECHJET 400
Phase of flight: Taxi
Anomaly: Aircraft Equipment Problem Critical

I was training a developmental on Ground Control when we were advised by the CIC of an Alert II emergency for an air carrier on about a 6 mile final for Runway 24R with a burning smell. Single emergency vehicle and fire trucks then called for driving permission to their predetermined Runway 24R positions. Both vehicles were given instructions to hold short of Runway 24L by my trainee. As the vehicles were approaching Runway 24L I coordinated with the Local Controller to cross Runway 24L with the emergency vehicles. I was surprised when Local told me he had an aircraft rolling on Runway 24L when we needed to get the emergency vehicles to Runway 24R and I could cross behind the departing aircraft. We then crossed single emergency vehicle at Taxiway S first and a little later fire trucks at Taxiway K; by now our emergency aircraft was landing on Runway 24R. The emergency vehicles proceeded to hold short of Runway 24R not realizing the emergency aircraft had just landed and was holding short of Runway 24L at Taxiway N. Single emergency vehicle then asked if the emergency aircraft was next to land and I told them the aircraft had landed and was holding short of Runway 24L at N. I then told the vehicles they could drive either via Taxiway G or C; which kept them between the runways; to the aircraft. Local then told us the pilot wanted the vehicles to check his right engine before proceeding any farther. The aircraft was still holding short of Runway 24L at N. All vehicles were near the aircraft between the runways on Taxiway N. Fire trucks was told about the right engine check the pilot wanted. We then talked to some other ground aircraft when we heard the CIC yell out about an ARFF vehicle near Runway 24L and Taxiway N as Local had just given a take off clearance on Runway 24L. When I looked towards that intersection I saw an ARFF vehicle at the edge of Taxiway N headed Westbound away from the runway. The AMASS alert system never went off because the departing aircraft had barely started his take off roll. We had then known either a pilot deviation; runway deviation or something had possibly happened. We later learned through all the confusion that neither single emergency vehicle nor fire trucks ever reported verbally clear of Runway 24L after the initial Runway 24L crossing as they should by the LOA. We are now waiting to hear the outcome from all of this. Although the vehicles never reported clear everyone in the tower saw them clear of Runway 24L; then holding short of Runway 24R; then drive via Taxiway G and/or C to the aircraft holding between the runways. We think the ARFF vehicle never should have gone back onto Runway 24L without permission; approximately 3 minutes after the initial crossing and just because they never reported clear of Runway 24L; but everyone saw them clear; doesn't mean Runway 24L is still theirs. And the last clearance given to them was drive via Taxiway G or C to the aircraft holding short of Runway 24L at N. Anytime an emergency is in progress possibly stopping all other traffic from departing or arriving other runways ASAP to allow emergency equipment to get to their positions and continue until all emergency equipment are all clear again. This incident happened more because of aircraft continuing to depart when emergency vehicles were around the runway environment before and after the emergency aircraft landing. Tower Ground Controller described an emergency event when Local Control cleared an aircraft off a parallel runway with emergency equipment trying to get to the emergency aircraft followed by complete confusion regarding vehicle runway clearance reports.